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We perform a rigorous, diffraction-based two-dimensional analysis to develop an analytical expression for the point spread function (PSF) of the multiple Bracewell interferometric (in-line, even-numbered multi-aperture) configurations proposed for extrasolar planet detection. The number of apertures, total length of interferometer array, and the diameter and shape of individual apertures control the PSF. We show that there are theoretically just a few points where the PSF is zero for monochromatic radiation. These zero-irradiance points disappear due to the spectral width of the source spectrum. When including, also, the finite spatial extend of the source, it is impossible to detect an image of a planet with just a two-aperture interferometer. This analysis further demonstrates that the so-called nulling interferometric techniques decrease the amount of detected radiation originating at the bright star by the same factor as that emitted by the planet.

Point spread function of (multiple) Bracewell interferometric configuration(s) and the nulling hypothesis in planet detection